1. Course Grade

• Course grades were curved a little, but not much.

  94   - 100   A
  89.5 - 93.9  A-
  86   - 89.4  B+
  83   - 86.4  B
  78   - 82.9  B-

2. Final

• The final was graded out of 50 points.  Out of 24 people who took the exam, the median was 46.8.  Score distribution was

  45 - 50    14
  40 - 44.5   7 
  35 - 39.5   1
  29 - 34.5   2

• Comments on some questions which several people made mistakes.
  • Question 2 (a)

    for i := 1 to 2n do
      for j := 1 to 2n do
        x := x + 1

    The number of execution is 4n². 

     

  • Question 2 (b)

    i := n
    while i >= 1 do
      begin
      for j := 1 to n-1 do
        x := x + 1
      i := i / 2
      end

    The number of execution is (lgn + 1)(n - 1).  Several people seem to have thought the j's index goes up to i - 1 instead of n - 1.

     

  • Question 5

    Prove that, if f(x) = O(g(x)), then f(x) + g(x) = O(g(x)).

    Many people said f(x) <= c1*g(x) and g(x) <= c2*g(x).  The second one is NOT assumed in the question.  I only gave a full credit if you explicitly stated the assumption that g(x) = O(g(x)).  Also, many answers had something like  g(x) <= c2*x.  That's incorrect.

     

  • Question 6

    T(n) = 3*T(n-1) - 2*T(n-2)

    Some people tried (unsuccessfully) to use iteration method.  This form requires the characteristic equation method.